Confidence intervals for comparing two scale parameters based on levene statistics

Abstract

The problem of comparing the scales of two populations arises in a variety of areas. Robust confidence intervals and tests for (the logarithm of) the ratio of the two population standard deviations have been studied over the past four decades. Levene statistics and Fligner-Killeen rank statistics are two well-known competitors. Recently, Hall and Padmanabhan (1997) improved the rank-based Fligner-Killeen procedures using bootstrap and adaption. This paper explores potential improvement of Levene type procedures by considering bootstrap and/or adaption methods. Several non-traditional bootstrap intervals based on Levene statistics are proposed and compared with traditional ones. Adaptive procedures using the best bootstrap interval found in this study are also investigated. All the procedures based on Levene statistics are compared with those based on Fligner-Killeen rank statistics.

Keywords:

• Adaptive Procedure
• Bootstrap
• Rank Test
• Robustness